MIND-CHANGING MATHEMATICS: John Allen Paulos
reviews Sharon Bertsch McGrayne's
The Theory That Would Not Die, subtitled – perhaps fittingly, in an age when subtitles have become breeding grounds for circumlocution – "How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines and Emerged Triumphant From Two Centuries of Controversy."
Bayes’s theorem, named after the 18th-century Presbyterian minister
Thomas Bayes, addresses this selfsame essential task: How should we
modify our beliefs in the light of additional information? Do we cling
to old assumptions long after they’ve become untenable, or abandon them
too readily at the first whisper of doubt? Bayesian reasoning promises
to bring our views gradually into line with reality and so has become an
invaluable tool for scientists of all sorts and, indeed, for anyone who
wants, putting it grandiloquently, to sync up with the universe. If you
are not thinking like a Bayesian, perhaps you should be.
Apparently it's actually been rather handy, despite its initial appearance of uselessness.
McGrayne devotes much of her book to Bayes’s theorem’s many remarkable
contributions to history: she discusses how it was used to search for
nuclear weapons, devise actuarial tables, demonstrate that a document
seemingly incriminating Colonel Dreyfus was most likely a forgery,
improve low-resolution computer images, judge the authorship of the
disputed Federalist papers and determine the false positive rate of
mammograms. She also tells the story of Alan Turing and others whose
pivotal crypto-analytic work unscrambling German codes may have helped
shorten World War II.
Mathematics has never been a point of great interest for me, so I'll leave the probability work to you. Although, for those of us considered somewhat less than mathematically inclined, McGrayne is quick to include simple examples, retold skilfully and concisely by Paulos. Take a look at the
full article.
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